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Yakvenalex [24]
3 years ago
9

What number must you add to complete the square x^-8x=39

Mathematics
2 answers:
dem82 [27]3 years ago
6 0

Answer:

The number must be added to complete the square is  16

Step-by-step explanation:

It is given that,

x^2 - 8x = 39    ------(1)

The quadratic equation is of the form ax^2  + bx + c =0

To complete the square we have to add (b/2)^2 and subtract (b/2)^2

Therefore the eq (1) becomes

here b= -8, so we have to add (8/2)^2 = 4^2 = 16

Therefore the number is 16

<u>To find x</u>

x^2 - 8x  = 39

Add 16 to both sides

x^2 - 8x +16  = 39 + 16

(x - 4)^2 = 55

x - 4 = √55

x = √55 -4

notsponge [240]3 years ago
3 0

Answer:

Given equation: x^2-8x =39

when we complete the square , we take half of the value of 8 , then square it, and added to the left sides, we get;

x^2-8x+4^2 = 39 +4^2

∵8 is the value (\frac{8}{2})^2

Notice that, we add this both sides so that it maintains the equality.

then;

x^2-8x+4^2 = 39 +4^2

(x-4)^2 = 39 + 16   [ (a-b)^2 = a^2-2ab+b^2 ]

Simplify:

(x-4)^2 =55

The number must be added to complete the square is, 4^2 = 16



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40 points and I will choose brainlyist <br><br> below is the question.
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Using proportions, the expected number of adults in Palm City whose main source of news is the internet or newspaper is of 19,413.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the table, the proportion of adults in Palm City whose main source of news is the internet or newspaper is found as follows:

p = (62 + 88)/(62 + 88 + 128 +24 + 38) = 0.4412.

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2 years ago
Jack is flying his kite . He runs 100 feet away from his house and lets out 45 feet of string . The angle of elevation from the
fiasKO [112]

Answer: 125.80 ft

Step-by-step explanation:

Asuming the described situation is as shown in the figure below, we need to find the distance h between the kite and Jacks house, but first we need to find the x, y and then d.

How?

We will use trigonometry, especifically the trigonometric functions sine and cosine:

For y:

sin(65 \°)=\frac{y}{45 ft} (1)

Where y is the opposite side to the angle and 45 ft the hypotenuse.

Isolating y:

y=40.78 ft (2)

For x:

cos(65 \°)=\frac{x}{45 ft} (3)

Where x is the adjacent side to the angle.

Isolating x:

y=19.017 ft (4)

Finding d:

d=x+100 ft (5)

d=19.017 ft +100 ft

d=119.017 ft (6)

Now that we have found these values, we have to work with a bigger triangle, where the hypotenuse is the distance between the kite and Jack's house h and the sides are the values calculated in (4) and (6).

So, in this case we will use the <u>Pithagorean theorem</u>:

h^{2}=y^{2} +d^{2} (7)

Isolating h and writing with the known values:

h=\sqrt{y^{2} +d^{2}} (8)

h=\sqrt{(19.017 ft)^{2} +(119.017 ft)^{2}} (9)

h=125.80 ft This is the distance between the kite and the house

3 0
3 years ago
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